Docs: read the landing page release badge from the app repository

[SandObserver]

Summary

• Add readAppVersion() to src/lib/repo.ts, reading version from the app repository's api/package.json and returning null when the checkout or the manifest is unreadable.
• Render the landing page footer release badge from that value instead of a hand-typed string, and carry it in a data-version attribute.
• Add a verbadge rule to scripts/check-dist.mjs that fails the build when dist/index.html ships without a semver release badge, matching how the generated pages are already gated.

Testing
All green: npm run build and npm run check both pass with STACKYARD_REPO set, and the badge renders v1.7.1 from api/package.json. Building with the checkout absent makes the new rule fail with exit 1, verified. Footer measured in Chrome in both colour schemes: badge geometry is unchanged at 107x23.

Checklist

• npm run build and npm run check both pass.
• Product UI is shown by running or capturing it, never recreated in CSS.
• Any new preview or screenshot carries no private hostnames or real data.
• Visual changes verified in both colour schemes and both docs themes.
• Links to the app repo still resolve.

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